Question 1062609
if the ratio of the sides of 2 polygons is 5/7, then the ratio of the area of the two polygons is (5/7)^2 and the ratio of the volume of the two polygons is (5/7)^3.


the volume of your smaller polygon is 35 cm^3.


let x be the volume of your larger polygon.


then (5/7)^3 * x = 35


solve for x to get x = 96.04 cm^3.


the surface area of your polygon is divided into two parts.


the formula is equal to pi * r^2 + pi * r * l, where l is the small letter L which represents the slant height.


the ratio of the surface area of the smaller cone is therefore equal to (5/7)^2 * pi * r^2 + (5/7)^2 * pi * r * l.


this formula can be made equivalent to (5/7)^2 * (pi * r^2 + pi * r * l).


if this is correct, then the surface area of the smaller cone should be equal to (5/7)^2 * the surface area of the larger cone.


i tested this out with an online calculator and determined that it is correct.


you can do the same, using the following online calculator.


<a href = "http://ncalculators.com/area-volume/cone-calculator.htm" target = "_blank">http://ncalculators.com/area-volume/cone-calculator.htm</a>



note that the calculator used the formula pi * r^2 + pi * r * sqrt(r^2 + h^2).


this is because l is equal to sqrt (r^2 + h^2), therefore, they just replace l with sqrt(r^2 + h^2).


the calculator confirms thqt the volume of the smaller cone is equal to (5/7)^3 * the volume of the larger cone, and it confirms that the surface area of the smaller cone is equal to (5/7)^2 * the area of the large cone.


i used the following measurements when testing.


radius of smaller cone is 5.
height of smaller cone is 10.


radius of larger cone is 7.
height of larger cone is 14.


you can see that the ratio of the corresponding sides are (5/7).


you can use whatever measures you see fit.


just make sure that the corresponding sides of the smaller cone are equal to 5/7 * the corresponding sides of the larger cone.